Subject: orbitals not observed

From: Eric Scerri <[email-masked]>
Date: Thu, 3 Aug 2000 22:39:16 -0800

Jan Labanowski has just suggested that I resend my article on whether or
not orbitals can be observed since many list members require text only
versions.

The article will appear in November's issue of Journal of Chemical Education.

I hope this works and that references are not lost.  Apologies for the
overload.

regards,

Article accepted and due to appear in Journal of Chemical Education, vol
77, November Issue, 2000.

Have Orbitals Really Been Observed?

Eric R. Scerri
Department of Chemistry,
Purdue University,  West Lafayette, IN 47907.
[email-masked]

Abstract.
The recent reports claiming to have observed textbook orbitals are analyzed
and it is argued that what was observed indirectly, and not for the first
time, was electron density.  It is also suggested that the tendency to
conflate of the terms electron density and orbital to mean the same thing
will give rise to confusion in chemical education.

Introduction
The purpose of this article is to comment on the pedagogical ramifications
of the recently claimed observation of d orbitals and the way in which
these results were first announced and subsequently reported (1-6).
	Atomic orbitals, their use in writing electronic configurations and
as a means of rationalizing so much of modern chemistry have, rightly or
wrongly, become completely ubiquitous in textbooks as well as the research
literature.  Orbitals have become part of the lingua franca of chemistry.
They represent one of chemistry's major paradigms, to use a much abused
term (7).  Surely it is essential that claims to having arrived at a new
understanding of such a crucially important educational concept should be
subjected to close scrutiny.  It is also essential for chemical educators
at all levels to take note of these developments in order to adjust their
teaching accordingly if such adjustments are necessary.  At the very least
educators should take some time to reflect on the meaning of such an
important concept as an atomic orbital when it is claimed that contrary to
previous beliefs they have now been observed for the first time.
        As often seems to be the case with startling new discoveries it
appears that the manner in which this finding has been communicated has
given rise to a certain amount of confusion, to say the least.  What is
surprising however is that in this particular case the initial mode of
communication was not a press conference, as in the infamous case of cold
fusion, but the publication of an article in the prestigious journal
Nature.
	I believe that the authors of this article come close to making the
claim that d orbitals have been literally observed when they write,
the correspondence between our experimental map and the classical diagrams
of dz2 orbitals sketched in textbooks is striking.  All our difference maps
show strong non-spherical charge distributions around the copper atoms,
with the characteristic shape of d orbitals... (1)

	What has exacerbated the situation has been an accompanying
editorial article with less, if any, reservations concerning the
identification of the images obtained with textbook orbitals.  The headline
caption for the editorial begins,

The classic textbook shape of electron orbitals has now been directly
observed. (2)

The main body of the article states that,

For the first time the striking shape of some of the electron orbitals is
revealed experimentally.  The paper by Zuo et al. is remarkable because the
quality of their charge-density maps allows, for the first time, a direct
experimental 'picture' to be taken of the complex shape of the dz 2 orbital.

	In addition, the front page of this issue of Nature featured the
simple words "Orbitals observed" in large bold letters, alongside some
images taken from the primary article.  Not surprisingly some more popular
accounts have not expressed any caution whatsoever in reporting the new
findings.  For example, a web page produced by a leading popular science
magazine boldly claims,

The idea of orbitals has long proved useful for describing atoms and their
interactions mathematically, but not physically.  Now all that's changed.
Researchers at Arizona State University recently published in Nature the
first true images of atomic orbitals in Cu2O, a crystal called cuprite.  (3)

	An article appearing in Chemical and Engineering News begins with,

Remember the really neat-looking d-orbital from freshman chemistry?  The
one that looks like a three dimensional figure 8 with a doughnut around its
midsection?  Well, it's just been experimentally observed by Scientists at
Arizona State University at Tempe.  (5)

	It should be borne in mind that this journal is directed at members
of the American Chemical Society and not just members of the interested
public.1

Theoretical Issues
Let me now turn to the theoretical status and limitations of orbitals and
why orbitals cannot possibly be observed.  Atomic orbitals are mathematical
constructs and strictly speaking are only genuine wavefunctions in
one-electron systems such as the hydrogen atom.  In many-electron atoms
orbitals serve as a useful approximation, as employed, for example,  in the
aufbau process to explain the features of the periodic system in an
approximate manner.   Atomic orbitals also serve as a means of classifying
spectroscopic transitions in the study of atomic spectra (8).
        The orbital approximation is the basis of a great deal of the work
conducted in quantum chemistry but here it is recognized that orbitals are
mathematical constructs which do not possess any independent physical
status.  According to quantum mechanics the assignment of four quantum
numbers to each electron in a many-electron atom, which is another way of
characterizing an orbital, is an approximation.  In fact only the atom as a
whole possesses well defined stationary states and these states are
characterized by the vectorial coupling of individual electronic momenta,
with different coupling schemes operating depending on whether or not
spin-orbit coupling is significant.
	In addition the usual textbook statements which refer to particular
numbers of electrons in particular orbitals, such as a 1s, 2p or 3d
orbitals, are in strict violation of the indistinguishability of electrons.
The latter requirement comes from the Pauli principle which maintains that
a physically admissible wavefunction for a system of fermions must be
antisymmetric with respect to exchange of the coordinates of any pair of
those fermions.  The indistinguishability of electrons is then an immediate
corollary of this basic fact.  These shortcomings of the orbital
approximation are counteracted, to some extent, by means of permutation of
all the electrons in the course of Hartree-Fock calculations.  If one
insists on retaining a physical picture this would correspond to regarding
each electron as being in every single orbital simultaneously.   But even
this permutation procedure does not succeed in including so-called dynamic
correlation between electrons and so doing requires the use of more
sophisticated mathematical techniques which go beyond the orbital
approximation.
        Of course the orbital model remains enormously useful as a first
approximation and lies at the heart of much of computational chemistry but
it is, just that, a model, as computational chemists and physicists are
well aware.  According to accepted current theory atomic orbitals serve
merely as basis sets, that is as types of coordinate systems which can be
used to expand mathematically the wavefunction of any particular physical
system.  Just as the coordinate system of x, y, and z used to describe any
particular experiment in classical physics is unobservable, so too atomic
orbitals are completely unobservable even in principle.

Observational Aspects
What can be observed, and indeed is frequently observed in experiments, is
electron density.  The observation of electron density is indeed a major
field of research in which several monographs and review articles have been
written (9).   However, an examination of this literature shows that
researchers consistently discuss the observation of electron density but
not of orbitals.
        In the recently reported experiments the authors have fit
experimental X-ray and electron diffraction data to a model called
multipole refinement.   This method does not assume an actual sum of atomic
contributions but fits the data by an expansion in terms of radial
functions multiplied by spherical harmonics on various centers.  The result
is a charge density which is then compared to that obtained as a
superposition of spherical atomic contributions assuming that the compound
is perfectly ionic.  The density difference map is thus obtained as the
difference between the experimental fit and the spherical or purely ionic
fit.
	In general, the result of experiments of this type, and their
subsequent analysis, is the total electron density which can be, and often
is, analyzed directly.  Moreover, in the case of molecular crystals or
metals there is of course no assumption that the compound be ionic.
        My aim is not to deny that the techniques reported may have thus
provided an image of overall electron density in the copper compounds in
question but only to question whether

The classic textbook shape of electron orbitals has now been directly
observed (2),

to cite again the editorial in Nature, and the suggested linking of the
images obtained with textbook 3d orbitals in the primary paper.
 	Although I may have appeared to absolve the primary authors
themselves from making the identification between the images they obtained
and textbook orbitals, I believe the situation to be more complicated.  If
these authors had wished to be cautious in the presentation of their
findings, it seems a little odd that they should have expressed their
findings in such a suggestive and as it has turned out rather misleading
manner.  It is also rather surprising that in all their quoted remarks,
which have appeared in other magazines, and even daily newspapers, the
authors have done nothing to deny, or at least diminish, the reports that
they have in fact directly observed some textbook orbitals.   If this is
due to a conflation of the terms "electron density" and "orbital" I suggest
that it should be resisted since such terms have precise meanings which
should be kept distinct.

Advice to Educators
My advice to chemistry educators is to avoid being seduced by the recent
reports and not to revise their long-held view that atomic orbitals are
just mathematical constructs.  Textbook orbitals will never be observed
although they will probably retain their great usefulness in many branches
of science.  Atomic orbitals should not be identified with electron density
since doing so can only lead to further confusion in such areas as
computational chemistry.
	In this rapidly expanding area major advances have taken place in
recent years.  Whereas the self-consistent field method for performing
atomic and molecular calculations was originally implemented through
various orbital methods, the density functional approach, which considers
electron density instead or orbitals and wavefunctions, has become
increasingly important and in fact computationally superior in the case of
large systems.  Many excellent reviews have been published on the
relationship between the traditional orbital ab initio methods and the more
recent density functional approaches (10).  In some of these approximation
methods such as the Kohn-Sham theories, for example, mixtures of both
approaches have been combined together while the Sham theory uses only
density functionals.  The point I am trying to emphasize is that it is
important to distinguish between orbitals and electron density at advanced,
as well as elementary, levels of chemical education.   The recent claim to
having observed orbitals conflates together the terms density and orbitals
density and only serves to blur this important distinction.

Direct and Indirect Observation
Readers might be wondering how the situation under discussion here relates
to the claims, which have now become fairly ubiquitous, regarding the
observation of atoms using scanning tunneling microscopy (STM) and atomic
force microscopy (AFM).   Of course it must be said that atoms are not
being directly observed in these studies since all that is really measured
is the flow of current across a tip, or the force that the tip exerts when
passing across a surface.  Is the question of the putative observation of
orbitals an analogous case and am I merely denying that orbitals can be
directly observed just like the case of atoms?
	My response to this question will be in two parts.   The situation
with the recent reports is analogous in the sense that electron density is
also being indirectly observed, and indeed more indirectly than atoms,
since the technique involves subtracting a reference state density which is
not the case in STM and AFM studies.2  The second part of my response is
that in the case of orbital observation there is simply no analogy with the
case of atoms.
	It is not just that orbitals cannot be directly observed but they
cannot be observed period.  Whereas there is nothing in the formalism of
quantum mechanics to forbid the observation of atoms, or electron density,
the same theory dictates that orbitals are not observables.  Of course the
theory may be incorrect but if so one would need to obtain some independent
evidence for its breakdown.  The authors of the Nature article clearly do
not believe that they have refuted quantum mechanics.

Conclusions
As is often the case in scientific research the appeal of realism seems to
be irresistible in some quarters and this is perhaps why the reports were
not seriously challenged or at least no objections were raised in letters
to the editors of any of the magazines which carried the story.  But it is
surely essential to be more discerning in attributing physical reality to
entities which are defined theoretically and which the theory itself
informs us do not exist physically.   It is also rather unfortunate that
popular science journals from which many chemical educators rightly draw
inspiration, as well as information, should have misrepresented the recent
findings.  But as I suggested earlier this is not entirely surprising in
view of the way that the results were first communicated.
	In case anyone is under the impression that the claimed observation
of orbitals is just a passing fad I should draw their attention to another
recent article entitled, "Seeing Molecular Orbitals". Here similar kinds of
conceptual errors are made in conflating the terms orbital and electron
density, although there is at least no claim to having observed textbook
orbitals (11).
	Finally, I might add that since beginning to write this article I
have become aware of two groups of researchers who have made related
objections to the original article in Nature as well as the accompanying
editorial.  Spackman and other senior colleagues in the International Union
of Crystallography have pointed out what they see as glaring errors in the
Nature editorial by Humphreys (12).
More recently a group in Germany led by Schwarz have raised numerous
objections against the primary article, including some similar comments to
mine involving the nature of atomic orbitals (13).

Acknowledgment.
I acknowledge the help of reviewers in formulating a description of the
recent experiments performed on copper compounds and other helpful
suggestions.  I also thank Philip Coppens (Buffalo) Barry de Boer
(Pennsylvania) John Spence (Arizona State) and Colin Humphreys (Cambridge)
for discussion on experimental aspects of observing electron density and
several quantum chemists for discussion on the theoretical status of atomic
orbitals.  They are Peter Gill (Nottingham), Brian Sutcliffe (Brussels),
Peter Taylor (San Diego) David Cook (Sheffield) and Eugen Schwarz (Siegen).

Notes.

1.	In fact the same magazine rated the 'observation' of orbitals as
	one of the five most significant events in chemistry for the
	year 1999 (6).  The Newsletter for the American Physical
	Society (APS News, vol 9, No. 4, 2000) likewise described the
	event at one of the highlights of the year in physics for 1999.
2.	The subtraction of reference state density is not an essential
	feature of the experimental electron density technique but a
	particular way of analysis which was used, for example, in the
	study by Zuo et al.

Literature Cited.

(1)	Zuo, J.M.; Kim, M.; O'Keeffe, M.; Spence, J.C.H. Nature,. 1999,
        401, 	49-52.
(2)	Humphreys, C.J. Nature, 1999,  401, 21-22.
(3)	Leutwyler, K.,
	http;//www.sciam.com/explorations/1999/092099cuprite/
(4)	Yam, P., Scientific American,  1999, 281, 30.
(5)	Jacoby, M. Chem & Eng. News. 1999, 77, 8-8.
(6)	Zurer, P., Chem & Eng. News. 1999, November 28, 38.
(7)	Scerri, E.R. J. Chem. Educ.  2000, 77,  522-525.
(8)	Condon, E.U; Shortley, G.H. The Theory of Atomic Spectra,
	Cambridge University Press, Cambridge, 1935.
(9)	Coppens, P., Hall, M.B., eds., Electron Distribution and the
	Chemical Bond, Plenum Press, New York, 1982,
	Coppens, P., X-Ray Charge Densities and Chemical Bonding,
	Oxford University Press, Oxford, 1997,
	Coppens, P., Ann. Rev. Phys. Chem, 1992, 43, 663-92.
(10)	Gill, P.M.W., in Encyclopedia of Computational Chemistry,  P. 	von
        Ragué Schleyer, ed., John Wiley, Chichester, 1998, vol. 1, 	678-689.
(11)	Pascual, J.I., Gómez-Herrero, J., Rogero, C., Baró, A.M., Sánchez-
	Portal, D., Artacho, E., Ordejón, P., Soler, J.M., Chem. Phys.
Lett. 	2000, 321, 78-82.
(12)	Spackman, M.A., Howard, J.A.K., Destro, R., International Union
	of Crystallography Newsletter, 2000, 8, 2-2.
(13)	Wang, S.G., Schwarz, W.H.E., Angew. Chem. Int. Ed.,  2000,
	39, 10, 1757-1762.

8

Eric Scerri PhD,
Visiting Professor,
Department of Chemistry,
Purdue University,
West Lafayette,
IN 47907
USA

tel:    765 496 1992

Editor: Foundations of Chemistry,

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Aspects of Chemistry.

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See also International Society for the Philosophy of Chemistry (ISPC)
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